The invention relates to a method for determining the torque of an induction machine, in which the stator terminal voltages and the stator terminal currents are used. This is preferably done by means of integration and subsequent high-pass filtering, to determine a filtered space vector, from which the DC component has thus been removed, of the concatenated stator flux. In addition, the invention relates to an associated device for carrying out a method, having a measurement device for detecting the stator terminal voltages and the stator terminal currents, and having a computation device for determining a filtered space vector of the concatenated stator flux.
For drive tasks with induction machines, it is important to know the torque developed by the induction machine, since such knowledge is the only way to specifically regulate the torque of the induction machine. By way of example, devices for determining the torque in such induction machines are known from DE 42 29 554 C2 and JP 56-79223 A, with the torque being formed by means of electronic components in what is known as a computation circuit. In both publications, electronic high-pass filters are used to suppress DC components when determining the concatenated stator flux.
Indirect torque control is known from EP 0 621 680 A1, in which the power in at least one of the three phases is regulated at a constant value. A disadvantage in this case is that no direct relationship can be specified between the power and the torque, so that the torque can necessarily be regulated only inaccurately using the known method.
A further method for determining the torque from the concatenated stator flux and the stator current, that is to say by measuring purely electrical variables and thus not using a separate torque sensor, is disclosed, for example, in DE 195 32 477 A1. The aim in this case is to regulate a torque of 0 by synchronizing the stator and rotor flux. In this case, the space vector of the concatenated stator flux revolves at the rotor angular velocity, so that the speed of the machine can be determined indirectly from the fundamental frequency of the supplying frequency-converter voltage. The cited document does not, however, describe how the concatenated stator flux is determined without accumulating errors which necessarily occur in the recording and processing of measured values and which lead to intolerable discrepancies when determining the torque.
The invention is now based on the object of specifying a method which is as simple and accurate as possible for determining the torque developed by the induction machine using only electrical variables, in which case the errors caused by numerical integration and the necessary high-pass filtering are largely corrected.
In addition, the invention is based on the object of specifying a device for carrying out the method.
According to the invention, the first-mentioned object is achieved by means of a method having the features of patent claim 1 for example. In the method according to the invention for determining the torque of an induction machine, the stator terminal voltages and the stator terminal currents are used, by means of numerical integration and subsequent high-pass filtering, to determine a filtered space vector of the concatenated stator flux. Further, the torque is calculated from this by multiplication by a complex correction factor. The multiplication by the complex correction factor corrects the amplitude and phase errors which are caused by numerical integration and high-pass filtering and are each related to the fundamental of the power supply system voltage. As such, a value of the flux concatenation is calculated which is substantially exact with respect to the amplitude and phase of the fundamental of the power supply system voltage.
The aforementioned tasks are achieved according to the invention in the case of a method of the type mentioned initially in that the space vector is multiplied by a complex correction factor and, after the multiplication, the torque is calculated by means of the correction factor. The associated device has a computation device by means of which, in addition to determining the filtered space vector, this is multiplied directly by a complex correction factor. Thus, it is once again possible to calculate the torque from the filtered space vector multiplied by the complex correction factor.
The high-pass filtering makes it possible to compensate for errors which occur firstly in the measurement of the current and voltage values and which, secondly, result from the fact that, since the temperature varies with the operating conditions, the value of the electrical resistance of the stator winding, which is required to calculate the stator flux, is not known exactly. Furthermore, the high-pass filtering compensates for any residual error in the integration, thus avoiding any remaining discrepancy or drift in the calculated concatenated stator flux, which would lead to a remaining and/or increasing error in the determination of the torque.
In detail, the following steps are carried out in one advantageous refinement of the method according to the invention:
a) The stator terminal voltages and the stator terminal currents are measured at predetermined time intervals,
b) the measured values of the stator terminal voltages and the stator terminal currents are used to calculate the space vector of the stator voltage and, respectively, the space vector of the stator current,
c) the space vector of the stator voltage and the space vector of the stator current together with an initial value for the space vector of the concatenated stator flux are used to determine, by numerical integration, an unfiltered space vector of the concatenated stator flux,
d) the unfiltered space vector of the concatenated stator flux is multiplied by a predetermined filter factor for high-pass filtering,
e) the filtered space vector, determined in this way, of the concatenated stator flux is used as the initial value for the next numerical integration step, and
f) is multiplied by a complex correction factor in order to calculate the present torque of the induction machine.
Thus, in this refinement of the method, a numerical integration method is used to determine the concatenated flux from current and voltage signals sampled at predetermined time intervals.
In one preferred refinement of the invention, the computation device includes a first computation unit for calculating and for storing the space vector of the stator voltage and the space vector of the stator current. It further includes a second computation unit for calculating the space vector of the concatenated stator flux by numerical integration from the stored space vectors of the stator voltage and of the stator current and from an initial value, which is stored in an initial value memory, for the space vector of the concatenated stator flux. A third computation unit is included, connected downstream therefrom, for multiplying the calculated space vector of the concatenated stator flux by a filter factor. Finally, a fourth computation unit is included for calculating the torque from the space vector of the stator current, the space vector of the corrected concatenated stator flux, the number of poles and a correction factor, with the filtered space vector of the concatenated stator flux being passed to the input of the initial value memory.
In a further advantageous refinement of the invention, a control device is provided for controlling the torque of the induction machine as a function of the actual value, which is present at the output of the fourth computation device, of the torque.
The invention is based on equation (1), which is also used, by way of example, in DE 195 32 477 as the basis for the motor control system disclosed there and which makes it possible to calculate the torque from the concatenating stator flux and the stator current:
m=3/2xc2x7pxc2x7(xcexa8xe2x88x92xc3x97ixe2x88x92)xe2x80x83xe2x80x83(1)
While the space vector i∠ of the stator current can be determined directly from the measurable stator terminal currents i1,2,3 by using known coordinate transformations, the space vector xcexa8∠ of the concatenated stator flux must be determined indirectly from the terminal voltage u1,2,3 and the stator terminal currents i1,2,3.
The rate of change of the space vector xcexa8∠ of the concatenated stator flux is given by:                                           ⅆ                          Ψ              ∠                                            ⅆ            t                          =                              u            ∠                    -                      R            ·                          i              ∠                                                          (        2        )            
u∠xe2x80x94Space vector of the stator voltage
Rxe2x80x94electrical resistance of the stator winding and supply lines
The resistance R contained in equation (2) is either known as a parameter of the induction machine, or can be measured on the machine.
Finally, the space vector of the concatenated stator flux of the induction machine is obtained by integration as follows:                               Ψ          ∠                =                              ∫                          t              =              0                        t                    ⁢                                    (                                                u                  ∠                                -                                  R                  ·                                      i                    ∠                                                              )                        ⁢                          xe2x80x83                        ⁢                          ⅆ              t                                                          (        3        )            
For an ideal induction machine connected to a balanced three-phase power supply system without any harmonics the flux concatenation once the transient processes in the complex numerical plane have decayed describes a circle with a voltage at the power supply system frequency and whose center coincides with the origin. If the machine is operated from frequency changers or three-phase controllers (soft starters), the flux concatenation space vector revolves at the frequency of the fundamental, with any harmonics being expressed as fluctuations about the circular shape.
The advantage of torque determination based on the equations (1), (2) and (3) is, in particular, that no information whatsoever about the induction machine is required apart from the resistance R, which can be determined easily, and the known number of pole pairs p.
The integration required in accordance with equation (4) is now preferably carried out numerically, for example with equidistant sampling based on the trapezoid rule:                                                         Ψ              ^                        k            ∠                    =                                    Ψ                              k                -                1                            ∠                        +                                                            Δ                  ⁢                                      xe2x80x83                                    ⁢                  t                                2                            ·                              (                                                                            ⅆ                                              Ψ                        k                        ∠                                                                                    ⅆ                      t                                                        +                                                            ⅆ                                              Ψ                                                  k                          -                          1                                                ∠                                                                                    ⅆ                      t                                                                      )                                                    ⁢                  
                ⁢                              Ψ                          k              -              1                        ∠                    ⁢                      xe2x80x83                    ⁢                      -                    ⁢                      xe2x80x83                    ⁢                      calculated  (filtered)  space  vector  of  the
concatenated  stator  flux  for  sample  step  k-1                          ⁢                  
                ⁢                                            Ψ              ^                        k            ∠                    ⁢                      xe2x80x83                    ⁢                      -                    ⁢                      xe2x80x83                    ⁢                      unfiltered  space  vector  of  the  concatenated  
stator  flux  for  the  sample  step  k                          ⁢                  
                ⁢                  Δ          ⁢                      xe2x80x83                    ⁢          t          ⁢                      xe2x80x83                    ⁢                      -                    ⁢                      xe2x80x83                    ⁢                      sample  test  width                                              (        4        )            
The rates of change             ⅆ              Ψ        k        ∠                    ⅆ      t        ,      xe2x80x83    ⁢            ⅆ              Ψ                  k          -          1                ∠                    ⅆ      t      
of the space vector xcexa8k,kxe2x88x921∠ of the concatenated stator flux for sample steps k and kxe2x88x921 are in this case determined directly from the space vectors Uk,k less than 1∠, ik,kxe2x88x921∠ of the stator terminal voltage and of the stator terminal current associated with these sample steps, using equation (2).
As already explained above, the unavoidable errors in the measurement of the current and voltage values, in the resistance R which is not known exactly (temperature influence) and in the residual error remaining with numerical integration methods leads to a remaining discrepancy and/or to drifting of the calculated concatenated stator flux, which is expressed in displacement of the flux concatenation circle from the origin of the complex numerical plane. In the end, this would lead to a remaining or increasing error in the determination of the torque.
In order to largely eliminate these undesirable effects, the numerically determined space vector of the concatenated stator flux is now, according to the invention, subjected to high-pass filtering. In the case of a numerical integration method, this is done by multiplication of the calculated space vector of the concatenated stator flux by a filter factor xcex7, where xcex7 is only a little less than or equal to 1, for each sample step:                               Ψ          k          ∠                =                  η          ·                      [                                          Ψ                                  k                  -                  1                                ∠                            +                                                                    Δ                    ⁢                                          xe2x80x83                                        ⁢                    t                                    2                                ·                                  (                                                                                    ⅆ                                                  Ψ                          k                          ∠                                                                                            ⅆ                        t                                                              +                                                                  ⅆ                                                  Ψ                                                      k                            -                            1                                                    ∠                                                                                            ⅆ                        t                                                                              )                                                      ]                                              (        5        )            
xcex7xe2x80x94filter factor to produce a high-pass filter
The filtered space vector xcexa8k∠, obtained in this way, for the concatenated stator flux is then used in a next step k+1 for calculating the unfiltered space vector, {circumflex over (xcexa8)}kxe2x88x921∠ in accordance with equation (4).
Equation (6) can be used to find the magnitude of the filter factor xcex7, with xcfx84 being a filter time constant which is preferably 1 to 10 times the power supply system period.                     η        =                  exp          ⁡                      (                          -                                                Δ                  ⁢                                      xe2x80x83                                    ⁢                  t                                τ                                      )                                              (        6        )            
xcfx84xe2x80x94filter time constant
For operation on a three-phase power supply system with any given fundamental circular frequency xcfx89, there is a constant error both in the amplitude and in the phase angle (angle in the complex numerical plane), which is referred to in the following text as the fundamental error in the flux concatenation, after decay of the transient disturbances between the fundamental of the space vector calculated in accordance with equation (5), of the concatenated stator flux (flux concatenation), and the actual fundamental of the flux concatenation which is present in the induction machine. In this case, it is irrelevant whether the induction machine is supplied directly from the three-phase power supply system, from a soft starter or three-phase converter, from a frequency changer or from other controllers.
The constant fundamental error is now compensated for by multiplication of the flux concatenation calculated in accordance with equation (5) by a constant, complex correction factor C∠ so that, as a modification to equation (1), the following relationship is used for calculating the torque m:
mk=3/2xc2x7pxc2x7(C∠xcexa8k∠xc3x97ik∠)xe2x80x83xe2x80x83(7)
C∠xe2x80x94complex correction factor to compensate for errors.
The correction factor C∠ when using the integration rule in accordance with equation (5) becomes:                               C          ∠                =                                                                                                                                                (                                                  η                          +                          1                                                )                                            ·                      sin                                        ⁢                                          xe2x80x83                                        ⁢                    β                                                                              cos                      ⁢                                              xe2x80x83                                            ⁢                      β                                        +                    1                                                  -                                  j                  ·                                      (                                          η                      -                      1                                        )                                                                              η                ·                β                                      ⁢                          xe2x80x83                        ⁢            where            ⁢                          xe2x80x83                        ⁢            β                    =                                    ω              ·              Δ                        ⁢                          xe2x80x83                        ⁢            t                                              (        8        )            
xcfx89xe2x80x94circular frequency of the fundamental, to which the correction factor C∠ is matched
If numerical integration methods other than that described in equation (5) are used, the complex correction factor C∠ must be adapted as appropriate.